1. Field of the Invention
The invention relates to tiles, more particularly to tiles and apparatuses, systems and methods for fabricating tiles and tile patterns.
2. Background Art
Conventionally tiles are utilized on floors, walls, furniture or the like to provide an ornamental surface. Often, when tiles are utilized on surfaces such as floors or furniture tops, these surfaces experience pedestrian traffic or wear from objects placed thereupon.
Conventional flooring patterns include simplified patterns and complex patterns. The simplified patterns include wooden flooring and tiles of a uniform polygonal shape, such as rectangular tiles. Neither of which require, nor are provided with, limited tolerances. Minimal gaps are permissible in wood flooring because they generally do not upset the aesthetic appearance of the flooring and the gaps flow in the direction of the flooring and the associated grain patterns. If undesired, such gaps are typically filled with a mixture of sawdust and adhesive that is stained to match the associated flooring. Conventional simplified tiles do not require limited tolerances, because they are generally fabricated from a ceramic, stone or similar material that requires spacing between adjacent tiles and a grout or tile adhesive disposed therebetween. Therefore, variances in tolerances are unnoticed because adjacent tiles do not actually mate with one another.
Conventional semi-complicated tile patterns are typically limited to basic geometric shapes, such as lines, circle arcs and the like, and are limited in tolerances as well. Ceramic or stone tiles are conventionally spaced to receive grouting or tile adhesive therebetween and therefore the lack of precision is unnoticed. In complex wooden tile patterns, such as tiling, flooring, inlays, borders, parquetry and marquetry, tolerances are lacking thereby generating visually noticeable gaps between adjacent tiles. These conventional complex wooden tile patterns are costly and labor intensive and any gaps exacerbate these difficulties by requiring filling in the gaps. The filling is a combination of sawdust and a wood adhesive or lacquer which is stained to create nebulous feature lines. Another difficulty presented in wood tiling is that wooden tiles have a tendency to change shape and size due to humidity, drying, application of finishing materials, or the like. Therefore, when wooden tiles are fabricated by a manufacturer to specific tolerances, these tolerances may change by the time the tiles have gone through channels of distribution and finally reach the user who subsequently installs the tiles.
Other manufacturing methods include waterjet cutting or laser cutting. Such methods are typically unavailable to general public consumers. These methods are also ineffective for some tile materials. Waterjet cutting can not hold a good tolerance in most applications, (e.g., plus or minus 0.015 inches for most materials). Additionally, wood tends to absorb water thereby swelling and resulting in an inaccurately cut tile. Laser cutting can provide a tighter tolerance but is dependent on the refractive index of the materials and the thickness of the material being cut. Wood has a poor refractive index, thereby resulting in an imprecisely cut tile.
Conventional jigs for woodworking are typically limited in scope, functionality, application, quality and tolerance thereby limiting these characteristics of the resultant workpiece. Additionally, conventional woodworking jigs are limited in range of variations and styles. A woodworker must select from a predetermined variety of jigs to machine a workpiece.
Many tile patterns comprise various geometrical shapes, which are derived from mathematics. Mathematically developed patterns known as tessellations are geometric patterns formed by congruent plane figures of one or more types. Tessellations include infinite tessellations, finite tessellations and metamorphosis tessellations. Infinite tessellations also known as two dimensional tessellations because they represent a planar geometry upon a planar surface and are generally derived from Euclidean mathematics. Finite tessellations, also known as three-dimensional tessellations, provide a representation of a three dimensional object illustrated upon a two dimensional surface. Finite tessellations are derived from Euclidian mathematics or non-Euclidean mathematics, such as hyperbolic mathematics, spherical mathematics, or the like. Finite tessellations illustrate, for example, a representation of an infinite tessellation formed about a sphere, yet represented as projected upon a two dimensional planar surface. Tessellations are appreciated by both mathematicians and artists and are commonly associated with the artistry of M. C. Escher.
Due to the complexity of tessellations, they are generally only found in artwork, engravings, prints, posters or the like. Difficulties in reducing tessellated patterns into interlocking tiles is apparent in the prior art. For example, artwork of M. C. Escher has been embodied by tiles such as the glazed tiles in the column at the New Girls' School, in the Hague, circa 1959 and the Tile Mural (First) Liberal Christian Lycum, the Hague, circa 1960. Both of these tile representations do not include a single tile for each geometrical representation. Rather, the geometrical pattern is formed upon conventional rectangular tiles and individual geometrical units are separated by grouted gaps in between adjacent tiles. The prior art has further evolved by providing concrete molds for generating tessellated paver stones that are generally interlocking; however, gaps are provided between adjacent stones as well.